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Analytic solutions for optimal statistical arbitrage trading

In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein-Uhlenbeck process. By framing the problem in
terms of the ¯rst-passage time of the process, we derive expressions for the mean and variance of the trade length and the return.We examine the problem of choosing
an optimal strategy under two di®erent objective functions: the expected return; and the Sharpe ratio. An exact analytic solution is obtained for the case of maximising
the expected return.